MATH SOLVE

2 months ago

Q:
# Given f(x)=x2+14x+40. Enter the quadratic function in vertex form in the box.

Accepted Solution

A:

For this case we have an equation of the form:

[tex]y = ax ^ 2 + bx + c [/tex]

This equation in vertex form is:

[tex]f (x) = a (x - h) ^ 2 + k [/tex]

where (h, k) is the vertex of the parabola.

We have the following function:

[tex]f (x) = x ^ 2 + 14x + 40 [/tex]

We look for the vertice.

For this, we derive the equation:

[tex]f '(x) = 2x + 14 [/tex]

We equal zero and clear the value of x:

[tex]2x + 14 = 0 2x = -14 x = -14/2 x = -7[/tex]

Substitute the value of x = -7 in the function:

[tex]f (-7) = (- 7) ^ 2 + 14 * (- 7) +40 f (-7) = -9[/tex]

Then, the vertice is:

[tex](h, k) = (-7, -9) [/tex]

Substituting values we have:

[tex]f (x) = (x + 7) ^ 2 - 9[/tex]

Answer:

The quadratic function in vertex form is:

[tex]f (x) = (x + 7) ^ 2 - 9[/tex]

[tex]y = ax ^ 2 + bx + c [/tex]

This equation in vertex form is:

[tex]f (x) = a (x - h) ^ 2 + k [/tex]

where (h, k) is the vertex of the parabola.

We have the following function:

[tex]f (x) = x ^ 2 + 14x + 40 [/tex]

We look for the vertice.

For this, we derive the equation:

[tex]f '(x) = 2x + 14 [/tex]

We equal zero and clear the value of x:

[tex]2x + 14 = 0 2x = -14 x = -14/2 x = -7[/tex]

Substitute the value of x = -7 in the function:

[tex]f (-7) = (- 7) ^ 2 + 14 * (- 7) +40 f (-7) = -9[/tex]

Then, the vertice is:

[tex](h, k) = (-7, -9) [/tex]

Substituting values we have:

[tex]f (x) = (x + 7) ^ 2 - 9[/tex]

Answer:

The quadratic function in vertex form is:

[tex]f (x) = (x + 7) ^ 2 - 9[/tex]